In each of the following exercises, verify the given statement carefully, proceeding step by step. Validate each step that involves an inequality by using some statement found in this section.
This exercise is used in Section 6.3. The positive part of an a ∈ R is defined by
and the negative part by
a) Prove that a = a+ − a− and |a| = a+ + a−.
b) Prove that
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